强光元件逆向哈特曼在位检测装置误差敏感因素分析与验证

王姗姗; 石峰; 乔硕; 徐博文; 郝群; 宋辞; 铁贵鹏; 田野; 翟德德; 彭星

doi:10.11884/HPLPB202335.220405

强光元件逆向哈特曼在位检测装置误差敏感因素分析与验证

doi: 10.11884/HPLPB202335.220405

王姗姗^1,,
石峰^2, ,,
乔硕²,
徐博文¹,
郝群^{1, 3},
宋辞²,
铁贵鹏²,
田野²,
翟德德²,
彭星²

1.
北京理工大学光电学院，精密光电测试仪器及技术北京市重点实验室，北京 100081
2.
国防科技大学智能科学学院，长沙 410073
3.
长春理工大学光电工程学院，长春 130022

基金项目: 国家重点研发计划项目（2021YFC2202403-2）；国家自然科学基金项目(62175259)

详细信息

作者简介:
王姗姗，wshan@bit.edu.cn

通讯作者:
石　峰，shifeng@nudt.edu.cn

中图分类号: TH74
计量
- 文章访问数: 360
- HTML全文浏览量: 131
- PDF下载量: 60
- 被引次数: 0
出版历程
- 收稿日期: 2022-11-30
- 修回日期: 2023-05-23
- 录用日期: 2023-05-27
- 网络出版日期: 2023-07-13
- 刊出日期: 2023-09-01

Error-sensitive factors analysis and verification for optical element in-situ measurement device based on phase measuring deflectometry

Wang Shanshan^1
,,
Shi Feng^{2
, ,},
Qiao Shuo²,
Xu Bowen¹,
Hao Qun^{1, 3},
Song Ci²,
Tie Guipeng²,
Tian Ye²,
Zhai Dede²,
Peng Xing²

1.
Beijing Key Laboratory for Precision Optoelectronic Measurement Instrument and Technology, School of Optics and Photonics, Beijing Institute of Technology, Beijing 100081, China
2.
College of Intelligence Science, National University of Defense Technology, Changsha 410073, China
3.
School of Opto-Electronic Engineering, Changchun University of Science and Technology, Changchun 130022, China

摘要

摘要: 针对基于强光元件高精度面形在位检测需求，开展了面形测量误差敏感因素仿真分析，进行了系统结构误差和温度误差对测量结果的影响研究，分析各类误差对测量面形误差的具体影响，设计并搭建在位检测系统，开展系统温度变化、系统重复性、系统稳定性等测量实验。研究结果表明：所建立的逆向哈特曼仿真检测模型可用于平面、球面、非球面、自由曲面等各类型被测面，各类影响因素对测量结果的影响主要体现在低频误差上，对高频误差的影响相对较小，搭建的在位检测系统6 h内测量面形误差PV值最大不超过68 nm（约λ/10），RMS值最大不超过15 nm（约λ/40）。
- 面形测量 /
- 在位检测 /
- 强光元件 /
- 误差分析 /
- 仿真模型
Abstract: Based on optical element’s high precision in-situ measurement requirements, this paper carries out the sensitive factor simulation analysis, studies the influence of systematic structural errors and temperature errors on the measurement results, and designs and builds an in-situ measurement device to carry out measurement experiments of system temperature change, system repeatability and system stability. The results show that the simulation detection model can be used for plane/spherical/aspherical/free surface, the influence on the measurement results is mainly reflected in the low frequency error, the high frequency error is relatively small, the maximum PV value of the measurement surface shape error does not exceed 68nm (about λ/10), and the maximum RMS value does not exceed 15 nm (about λ/40).
- shape measurement /
- in-situ measurement /
- optical element /
- error analysis /
- simulation model

HTML全文

图 1 数据传输流程图

Figure 1. Data transmission flow chart

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图 2 Zemax边缘光线追迹图

Figure 2. Edge ray tracing of Zemax

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图 3 不同k值对应测量面形误差

Figure 3. Different k values correspond to the measurement surface shape error

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图 4 不同k值对应面形误差

Figure 4. The surface shape errors corresponding to different k values

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图 5 图像发生器沿Z轴定位误差影响示意图

Figure 5. Schematic diagram of the influence of image generator positioning error along Z axis

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图 6 图像发生器沿Z轴正方向偏移0.01 mm引起的去倾斜后面形误差

Figure 6. De-skewed surface shape error caused by the image generator offsetting 0.01 mm along the positive direction of Z axis

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图 7 沿Z轴方向偏移引起的面形误差大小

Figure 7. Surface shape error caused by image generator’s offset along the Z axis direction

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图 8 面形误差对应Zernike系数

Figure 8. Zernike coefficients corresponding to surface shape error

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图 9 沿Z轴方向偏移引起的面形误差大小

Figure 9. Size of the surface shape error caused by the offset along the Z axis

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图 10 面形误差对应Zernike系数

Figure 10. Zernike coefficients corresponding to surface shape error

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图 11 k₁＞0和k₁＜0时采样点变化示意图

Figure 11. Schematic diagram of the change of sampling points when k₁ ＞ 0 and k₁ ＜ 0

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图 12 k₁＞0时探测器镜头畸变引起的斜率及面形误差

Figure 12. k₁＞0, slope and surface shape error caused by detector lens distortion

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图 13 探测器镜头畸变引起的面形误差大小

Figure 13. Surface shape error caused by lens distortion of detector

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图 14 面形误差对应Zernike系数

Figure 14. Zernike coefficients corresponding to surface shape error

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图 15 在位检测系统结构

Figure 15. In-situ detection system structure

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图 16 测量结果随时间变化图

Figure 16. Change of measurement results with time

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图 17 测量结果和温度随时间变化图

Figure 17. Measurement results of surface shape error and temperature variation with time

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表 1 图像发生器定位误差对测量结果影响

Table 1. Influence of image generator’s positioning error on the measurement results

direction	maximum surface shape error/nm		corresponding to Zernike coefficients
direction	PV	RMS	number of terms	number of main items	main types
along the X axis	77.2	10.1	2、5、8、15	5	45° primary astigmatism
along the Y axis	88.9	18.1	3、4、6、7、9	4、6	defocusing and 0° primary astigmatism
along the Z axis	152.7	30.6	3、4、6、7	4、6	defocusing and 0° primary astigmatism

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表 2 针孔光阑定位误差对测量结果影响

Table 2. Effect of pinhole diaphragm positioning error on measurement results

direction	maximum surface shape error/nm		corresponding to Zernike coefficients
direction	PV	RMS	number of terms	number of main items	main types
along the X axis	81.8	10.8	2、5、8、15	5	45° primary astigmatism
along the Y axis	94.2	19.1	3、4、6、7、9	4、6	defocusing and 0° primary astigmatism
along the Z axis	161.9	32.4	3、4、6、7	4、6	defocusing and 0° primary astigmatism

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表 3 探测器镜头畸变对测量结果影响

Table 3. Effect of detector lens distortion on measurement results

	influencing factor	maximum surface shape error/nm		corresponding to Zernike coefficients
	influencing factor	PV	RMS	number of terms	number of main items	main types
detector lens distortion (\|k₁\|=1×10⁻³)	pin-cushion distortion	155.3	24.9	3、4、6、11、12、28	4、6、11、12	defocusing, 0° primary astigmatism and higher-order aberrations
detector lens distortion (\|k₁\|=1×10⁻³)	barrel distortion	155.3	24.9	3、4、6、11、12、28	4、6、11、12	defocusing, 0° primary astigmatism and higher-order aberrations

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表 4 温度变化对测量结果影响

Table 4. Effect of temperature change on measurement results

influencing factor	maximum surface shape error/nm		corresponding to Zernike coefficients
influencing factor	PV	RMS	number of terms	number of main items	main types
image generator expansion	416.9	85.3	3、4、5、6、7	3、4、5	defocusing, 45° primary astigmatism, 0° primary astigmatism
detector expansion	99.7	20.4	3、4、6、7	4	focusing out
support structure expansion	4.9	1.0	3、4、6、7、9	4、6	defocusing and 0° primary astigmatism

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表 5 检测系统参数

Table 5. Detection system parameters

measurement serial number	PV/nm	RMS/nm	measurement serial number	PV/nm	RMS/nm
1	19.2	3.1	16	46.6	9.6
2	18.4	2.9	17	46.7	9.6
3	21.7	4.0	18	47.7	10.0
4	28.3	5.4	19	49.3	10.3
5	29.7	4.8	20	44.9	9.3
6	27.7	5.2	21	42.6	8.8
7	33.7	6.6	22	45.5	9.5
8	34.4	6.6	23	43.5	8.7
9	31.3	5.9	24	41.7	7.3
10	34.3	6.6	25	41.3	6.6
11	37.4	7.1	26	50.1	9.0
12	40.5	8.1	27	60.6	10.9
13	44.5	9.3	28	45.7	9.0
14	48.2	10.0	29	37.6	6.3
15	48.1	10.1	30	39.9	7.1

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参考文献(19)

[1]	张梦瑶, 田爱玲, 王大森, 等. 基于逆向优化策略的面形绝对检测平移量研究[J]. 中国激光, 2022, 49:1804003 doi: 10.3788/CJL202249.1804003 Zhang Mengyao, Tian Ailing, Wang Dasen, et al. Translation of surface shape absolute testing based on reverse optimization strategy[J]. Chinese Journal of Lasers, 2022, 49: 1804003 doi: 10.3788/CJL202249.1804003
[2]	侯溪, 张帅, 胡小川, 等. 超高精度面形干涉检测技术进展[J]. 光电工程, 2020, 47:200209 Hou Xi, Zhang Shuai, Hu Xiaochuan, et al. The research progress of surface interferometric measurement with higher accuracy[J]. Opto-Electronic Engineering, 2020, 47: 200209
[3]	Ye Meitu, Liang Jin, Li Leigang, et al. Simultaneous measurement of external and internal surface shape and deformation based on photogrammetry and stereo-DIC[J]. Optics and Lasers in Engineering, 2022, 158: 107179. doi: 10.1016/j.optlaseng.2022.107179
[4]	Su Peng, Wang Yuhao, Burge J H, et al. Non-null full field X-ray mirror metrology using SCOTS: a reflection deflectometry approach[J]. Optics Express, 2012, 20(11): 12393-12406. doi: 10.1364/OE.20.012393
[5]	Berger G, Petter J. Non-contact metrology of aspheric surfaces based on MWLI technology[C]//Proceedings of SPIE 8884, Optifab 2013. 2013: 88840V.
[6]	Anderson D S, Burge J H. Swing-arm profilometry of aspherics[C]//Proceedings of SPIE 2536, Optical Manufacturing and Testing. 1995: 169-179.
[7]	Wan Xinjun, Bin Boyi, Xie Shuping, et al. Development of an integrated freeform optics measurement system based on phase measuring deflectometry[C]//Proceedings of SPIE 10847, Optical Precision Manufacturing, Testing, and Applications. 2018: 1084710.
[8]	Guo Chunfeng, Hu Anduo. Three-dimensional shape measurement of aspheric mirrors with null phase measuring deflectometry[J]. Optical Engineering, 2019, 58: 104102.
[9]	Chaudhuri R, Papa J, Rolland J P. System design of a single-shot reconfigurable null test using a spatial light modulator for freeform metrology[J]. Optics Letters, 2019, 44(8): 2000-2003. doi: 10.1364/OL.44.002000
[10]	Fang Fengzhou, Zhang Xiaodong, Weckenmann A, et al. Manufacturing and measurement of freeform optics[J]. CIRP Annals, 2013, 62(2): 823-846. doi: 10.1016/j.cirp.2013.05.003
[11]	Lei Huang, Idir M, Zuo Chao, et al. Comparison of two-dimensional integration methods for shape reconstruction from gradient data[J]. Optics and Lasers in Engineering, 2015, 64: 1-11. doi: 10.1016/j.optlaseng.2014.07.002
[12]	Xu Yongjia, Gao Feng, Jiang Xiangqian. Enhancement of measurement accuracy of optical stereo deflectometry based on imaging model analysis[J]. Optics and Lasers in Engineering, 2018, 111: 1-7. doi: 10.1016/j.optlaseng.2018.07.007
[13]	Huang Lei, Ng C, Asundi A K. Dynamic 3D measurement for specular reflecting surface with monoscopic fringe reflection deflectometry[C]//Proceedings of the Computational Optical Sensing and Imaging 2011. 2011: CWC3.
[14]	Song Lei, Yue Huimin, Kim H, et al. A study on carrier phase distortion in phase measuring deflectometry with non-telecentric imaging[J]. Optics Express, 2012, 20(22): 24505-24515. doi: 10.1364/OE.20.024505
[15]	阮一郎, 李大海, 余林治, 等. 基于相位测量偏折术的成像透镜轴外点波像差测量[J]. 中国激光, 2022, 49:2104003 doi: 10.3788/CJL202249.2104003 Ruan Yilang, Li Dahai, Yu Linzhi, et al. Off-axis point wave aberration testing for imaging lens based on phase measuring deflectometry[J]. Chinese Journal of Lasers, 2022, 49: 2104003 doi: 10.3788/CJL202249.2104003
[16]	陈贞屹, 赵文川, 张启灿, 等. 基于立体相位测量偏折术的预应力薄镜面形检测[J]. 光电工程, 2020, 47:190435 Chen Zhenyi, Zhao Wenchuan, Zhang Qican, et al. Shape measurement of stressed mirror based on stereoscopic phase measuring deflectometry[J]. Opto-Electronic Engineering, 2020, 47: 190435
[17]	Su Peng, Khreishi M, Huang Run, et al. Precision aspheric optics testing with SCOTS: a deflectometry approach[C]//Proceedings of SPIE 8788, Optical Measurement Systems for Industrial Inspection VIII. 2013: 87881E.
[18]	Faber C, Olesch E, Krobot R, et al. Deflectometry challenges interferometry: the competition gets tougher![C]//Proceedings of SPIE 8493, Interferometry XVI: Techniques and Analysis. 2012: 84930R.
[19]	冯婕, 白瑜, 邢廷文. Zernike多项式波面拟合精度研究[J]. 光电技术应用, 2011, 26(2):31-34 doi: 10.3969/j.issn.1673-1255.2011.02.009 Feng Jie, Bai Yu, Xing Tingwen. Fitting accuracy of wavefront using Zernike polynomials[J]. Electro-Optic Technology Application, 2011, 26(2): 31-34 doi: 10.3969/j.issn.1673-1255.2011.02.009